Tohoku Mathematical Journal
2015
December
SECOND SERIES VOL. 67, NO. 4

Tohoku Math. J.
67 (2015), 541-551

Title ON THE DEAD-CORE PROBLEM FOR THE $p$-LAPLACE EQUATION WITH A STRONG ABSORPTION

Author Jong-Shenq Guo and Chin-Chin Wu

(Received November 5, 2013, revised July 29, 2014)
Abstract. We study an initial boundary value problem for the $p$-Laplace equation with a strong absorption. We are concerned with the dead-core behavior of the solution. First, some criteria for developing dead-core are given. Also, the temporal dead-core rate for certain initial data is determined. Then we prove uniqueness theorem for the backward self-similar solutions.

Mathematics Subject Classification. Primary 35K20; Secondary 35K55, 34B15, 34A12.
Key words and phrases. Dead-core, $p$-Laplace equation, strong absorption, self-similar solution.

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